Details

Time bar (total: 1.3m)

sample58.0ms

Algorithm
intervals
Results
15.0ms183×body80valid
12.0ms30×body1280valid
9.0ms256×pre80true
8.0ms26×body640valid
2.0ms9×body320valid
2.0ms8×body160valid

simplify146.0ms

Calls
1 calls:
Slowest
146.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize33.0ms

Local error

Found 2 expressions with local error:

1.9b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
26×add-sqr-sqrt
25×times-frac
19×distribute-lft-out
14×add-cube-cbrt
6×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-cbrt-cube add-exp-log add-log-exp
2×pow1 flip3-+ div-sub associate-/r/ flip-+ insert-posit16 associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- div-inv flip--
Calls
2 calls:
Slowest
173.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
31.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series142.0ms

Calls
2 calls:
Slowest
86.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
56.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.4s

Calls
74 calls:
Slowest
284.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
224.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
191.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
180.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
177.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))

prune727.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.4b

localize21.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
101×*-un-lft-identity
64×add-sqr-sqrt
44×frac-sub
42×times-frac
34×add-cube-cbrt
28×associate-/r*
25×flip3-- flip--
24×distribute-lft-out associate-/l/
22×associate-/l*
16×distribute-lft-out--
12×difference-of-squares
11×add-log-exp
8×add-cbrt-cube add-exp-log
6×clear-num frac-2neg
4×pow1 sub-neg diff-log insert-posit16 associate--r+
3×div-sub
2×cbrt-undiv div-exp associate-/r/ div-inv
1×flip3-+ flip-+ associate--r-
Calls
4 calls:
Slowest
841.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
406.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
168.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
39.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series361.0ms

Calls
4 calls:
Slowest
104.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
89.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
86.0ms
(/ alpha (+ (+ alpha beta) 2.0))
82.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

simplify27.6s

Calls
190 calls:
Slowest
1.1s
(- (* 1 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (/ (+ (+ alpha beta) 2.0) beta) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))
653.0ms
(- (* 1 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (/ (+ (+ alpha beta) 2.0) beta) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))
648.0ms
(- (* 1 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (/ (+ (+ alpha beta) 2.0) beta) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))
620.0ms
(- (* 1 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (/ (+ (+ alpha beta) 2.0) beta) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))
570.0ms
(- (* (sqrt beta) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (/ (+ (+ alpha beta) 2.0) (sqrt beta)) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize9.0ms

Local error

Found 4 expressions with local error:

11.5b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity frac-sub
48×log-div
39×add-sqr-sqrt
37×flip3-- flip--
30×associate-/r*
24×exp-diff
19×add-cube-cbrt
18×distribute-lft-out associate-/l*
14×log-prod
12×add-log-exp
10×distribute-lft-out--
8×difference-of-squares
7×exp-sum
6×pow1 clear-num frac-2neg
5×add-exp-log
4×exp-prod times-frac add-cbrt-cube diff-log insert-posit16
3×sub-neg
2×log-pow associate--r+ rem-exp-log
1×rem-log-exp associate--r-
Calls
4 calls:
Slowest
466.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
391.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
363.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
192.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series441.0ms

Calls
4 calls:
Slowest
172.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
112.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
87.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
70.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))

simplify29.4s

Calls
141 calls:
Slowest
723.0ms
(exp (log (- (* (/ beta (sqrt (+ (+ alpha beta) 2.0))) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (sqrt (+ (+ alpha beta) 2.0)) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))))
712.0ms
(exp (log (- (* 1 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (/ (+ (+ alpha beta) 2.0) beta) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))))
709.0ms
(log (- (* (sqrt beta) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (/ (+ (+ alpha beta) 2.0) (sqrt beta)) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))))
706.0ms
(log (- (* 1 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (/ (+ (+ alpha beta) 2.0) beta) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))))
654.0ms
(exp (log (- (* 1 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (/ (+ (+ alpha beta) 2.0) beta) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))))

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize26.0ms

Local error

Found 4 expressions with local error:

11.5b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
1.9b
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
19×log-prod *-un-lft-identity
11×log-pow
10×exp-prod
9×pow1 exp-sum add-cube-cbrt
8×difference-of-squares
7×add-log-exp
6×add-exp-log distribute-lft-out--
5×log-div
4×times-frac add-cbrt-cube insert-posit16
3×flip3-- exp-diff rem-log-exp flip--
2×sub-neg rem-exp-log
1×diff-log
Calls
4 calls:
Slowest
722.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
621.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
276.0ms
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
165.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series528.0ms

Calls
4 calls:
Slowest
182.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
141.0ms
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
112.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
93.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))

simplify4.8s

Calls
57 calls:
Slowest
281.0ms
(exp (* (cbrt (log (- (/ beta (+ (+ alpha beta) 2.0)) (log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))) (cbrt (log (- (/ beta (+ (+ alpha beta) 2.0)) (log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))))
210.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
204.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
195.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
190.0ms
(log (- (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (* (log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.7b

regimes191.0ms

Accuracy

75.4% (3.2b remaining)

Error of 6.0b against oracle of 2.9b and baseline of 15.7b

bsearch70.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
742.0ms8000×pre80true
530.0ms5851×body80valid
473.0ms899×body1280valid
239.0ms678×body640valid
86.0ms367×body320valid
33.0ms205×body160valid